The petition, set up by William Oliver Healey, states: "We the undersigned call upon [the UK] Government to implement a rule that if the Remain or Leave vote is less than 60%, based on a turnout less than 75%, there should be another referendum."

Meanwhile, Cornwall in southwest England -- a region which voted to leave the EU -- is now seeking confirmation from government ministers that it will keep getting funding equal to its previous EU allocation.

"Now that we know the UK will be leaving the EU we will be taking urgent steps to ensure that the UK Government protects Cornwall's position in any negotiations," said John Pollard, the leader of Cornwall Council.

"We will be insisting that Cornwall receives investment equal to that provided by the EU program which has averaged £60m (more than $82 million) per year over the last ten years."